Using the reciprocal services method, which of the following equations represents the algebraic expressions for the two equations needed to capture the total costs of a Janitorial Department (J) that includes not only $500,000 of direct costs but also 20% of the Maintenance Department (M) cost and a Maintenance Department that includes not only $250,000 of direct costs but also 40% of the Janitorial Department? (Hint: This equation is derived from the two separate equations representing each department's costs.)

a. J = ($500,000 × 0.20) + [($250,000 × 0.20) + J]

b. J = $500,000 – (0.20 × $250,000) – (0.20 × J)

c. J = $500,000 + [(0.20 ÷ $250,000) + (0.40 ÷ J)]

d. J = $500,000 + {0.20 × [$250,000 + (0.40 × J)]}

The equation that represents the algebraic expressions for the two equations needed to capture the total costs of the Janitorial Department is:

d. J = $500,000 + {0.20 × [$250,000 + (0.40 × J)]}

Explanation:

a) Data and Calculations:

                                                 Direct costs   Percent of Service Dept.

Janitorial Department (J)          $500,000          20% of M

Maintenance Department (M)  $250,000          40% of J

b) The reciprocal services method reapportions the costs of the service departments to other service departments using a system of simultaneous equations.  With its complications, the reciprocal method is the most accurate and equitable method for apportioning service departments' costs to production departments.

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